A continuously expanding Mongol Empire without any succession crisis.
An expanded Union of Soviet Socialist Republics integrating all other communist states.
Or what about a united Islamic empire, if there was no Shia-Sunni split?
Personally I would have liked to see a personal union between Sweden and England through the marriage of Erik XIV and Elizabeth I. If only the union could endure the infighting of the Vasa sons, it would have great potential for conquest both as a colonial power and on the continent; with such additional manpower combined with his own military reforms and tactical brilliance, Gustav II Adolf (assuming he would come to power in this scenario) could have run over the Holy Roman Empire and claimed the throne of all of Germany, the English navy would completely neutralize Denmark as a threat, and further Swedish expansion into Poland and Russia would be a piece of cake. It may only take a few decades for the union to put half of Europe under their banner, if everything goes smoothly.
Is there a rule that a single government has to by tyrannical? Without war it may be a utopia (trying not to laugh). Alternatively you could argue multiple governments competing in space would be anarchy. They would go to war with each other and destroy the colonies before there finished.
Plenty of totalitarian socialist governments achieved tyranny within their own borders without going into full scale wars. Imagine living in a global North Korea.
Just the prospect of ruling over everyone will attract very unpleasant characters to the top.
What is the largest country that can exist and how could it come to existance?
In my opinion the most likely:
A British Empire that defeats the American Revolution.
The Iberian Union survives.
The Franco-British Union becomes reality.
A more successful Napoleon or the mongols.
Axis win the ww2.
A unified caliphate.
A union between the soviet union, china and their satellite states
In all honesty, I think an expansionist Roman Empire if Trajan survived his Parthian campaign or the French Empire under that brilliant military genius Napoleon would be the two most likely choices for the world's largest possible nation.
Perhaps if the Mongolian civil war didn’t happen in the era of Kublai Khan, then the Mongols may have continued to dominate the most land an Empire ever ruled. Seriously, it was Mongolia, Russia, China, and the Persian Empire all in one. Under Kublai, the Yuan Dynasty ruled all of the East; the rest of Russia under the Golden Horde, and the Persian Empire (Eastern and Central Arabian Empire) was split into the Ilkhanate and Chagatai Khanate. The Mongol Empire was so large in land area that the 4 successor states were each larger than the Roman Empire at its widest extent.
As a comment on the Romans, while they were good in the mediterranean, their expanded territories beyond were incredibly problematic for them. Their attempts at expanding far beyond were regularly met with an inability to hold the land. The Rhine-Danube frontier was already difficult enough (and failed in the 3rd, 4th, and 5th centuries) and that’s a natural barrier. Expanding into Steppe regions was something the Romans were incapable of, they had no capability of holding the land without aligning themselves to Steppe tribes. The Romans almost always used outside forces against each other (in their many civil warfare) instead of for expansionistic purposes.
The largest nation possible would be if some empire conquered all the Earth, and then over generations, centuries, and millennia, the population of the countless subordinate ethnic groups al assimulatd into the dominate ethnic group and the realm stopped being an empire ruling all ethnic groups and became a nation ruling one single ethnic group that happened to include every human.